Uncertain Dynamic Responses of Fuzzy Arbitrary Order Damped Beam

Abstract

Uncertain dynamic responses of fuzzy fractionally damped beams have been studied using the newly developed double parametric form of fuzzy numbers subject to unit step and impulse loads. Uncertainties are assumed to be present in the initial conditions, and these are modeled through triangular convex normalized fuzzy sets. Using the alphacut form, the corresponding beam equation is first converted to an intervalbased fuzzy equation. Next, it has been transformed to crisp form by applying a doubleparametric form of fuzzy numbers. Finally, homotopy perturbation method (HPM) has been used to solve the same for obtaining the general fuzzy responses. Various numerical examples are taken into consideration. The results are plotted.